The complex dynamics of the Logistic map via two types of periodic impulsive forces is investigated in this paper. With the parameter varying, the system produces the phenomenon such as equilibrium solutions, periodic solutions, and chaotic solutions. Furthermore the system can evolve into chaos by a cascading of period-doubling bifurcations. The Poincaré map of the Logistic map via periodic impulsive force is constructed and its bifurcation is analyzed. Finally, the Floquet theory is used to explore the bifurcation mechanism for the periodic solutions.